// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <Eigen/Geometry>
#include <Eigen/LU>
#include <Eigen/SVD>

/* this test covers the following files:
   Geometry/OrthoMethods.h
*/

template<typename Scalar>
void
orthomethods_3()
{
	typedef typename NumTraits<Scalar>::Real RealScalar;
	typedef Matrix<Scalar, 3, 3> Matrix3;
	typedef Matrix<Scalar, 3, 1> Vector3;

	typedef Matrix<Scalar, 4, 1> Vector4;

	Vector3 v0 = Vector3::Random(), v1 = Vector3::Random(), v2 = Vector3::Random();

	// cross product
	VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1));
	VERIFY_IS_MUCH_SMALLER_THAN(v1.dot(v1.cross(v2)), Scalar(1));
	VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v2), Scalar(1));
	VERIFY_IS_MUCH_SMALLER_THAN(v2.dot(v1.cross(v2)), Scalar(1));
	VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(Vector3::Random()).dot(v1), Scalar(1));
	Matrix3 mat3;
	mat3 << v0.normalized(), (v0.cross(v1)).normalized(), (v0.cross(v1).cross(v0)).normalized();
	VERIFY(mat3.isUnitary());

	mat3.setRandom();
	VERIFY_IS_APPROX(v0.cross(mat3 * v1), -(mat3 * v1).cross(v0));
	VERIFY_IS_APPROX(v0.cross(mat3.lazyProduct(v1)), -(mat3.lazyProduct(v1)).cross(v0));

	// colwise/rowwise cross product
	mat3.setRandom();
	Vector3 vec3 = Vector3::Random();
	Matrix3 mcross;
	int i = internal::random<int>(0, 2);
	mcross = mat3.colwise().cross(vec3);
	VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));

	VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(vec3)).diagonal().cwiseAbs().sum(), Scalar(1));
	VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(Vector3::Random())).diagonal().cwiseAbs().sum(),
								Scalar(1));

	VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * mat3.colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1));
	VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * Matrix3::Random().colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1));

	mcross = mat3.rowwise().cross(vec3);
	VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));

	// cross3
	Vector4 v40 = Vector4::Random(), v41 = Vector4::Random(), v42 = Vector4::Random();
	v40.w() = v41.w() = v42.w() = 0;
	v42.template head<3>() = v40.template head<3>().cross(v41.template head<3>());
	VERIFY_IS_APPROX(v40.cross3(v41), v42);
	VERIFY_IS_MUCH_SMALLER_THAN(v40.cross3(Vector4::Random()).dot(v40), Scalar(1));

	// check mixed product
	typedef Matrix<RealScalar, 3, 1> RealVector3;
	RealVector3 rv1 = RealVector3::Random();
	VERIFY_IS_APPROX(v1.cross(rv1.template cast<Scalar>()), v1.cross(rv1));
	VERIFY_IS_APPROX(rv1.template cast<Scalar>().cross(v1), rv1.cross(v1));
}

template<typename Scalar, int Size>
void
orthomethods(int size = Size)
{
	typedef typename NumTraits<Scalar>::Real RealScalar;
	typedef Matrix<Scalar, Size, 1> VectorType;
	typedef Matrix<Scalar, 3, Size> Matrix3N;
	typedef Matrix<Scalar, Size, 3> MatrixN3;
	typedef Matrix<Scalar, 3, 1> Vector3;

	VectorType v0 = VectorType::Random(size);

	// unitOrthogonal
	VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
	VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));

	if (size >= 3) {
		v0.template head<2>().setZero();
		v0.tail(size - 2).setRandom();

		VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
		VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));
	}

	// colwise/rowwise cross product
	Vector3 vec3 = Vector3::Random();
	int i = internal::random<int>(0, size - 1);

	Matrix3N mat3N(3, size), mcross3N(3, size);
	mat3N.setRandom();
	mcross3N = mat3N.colwise().cross(vec3);
	VERIFY_IS_APPROX(mcross3N.col(i), mat3N.col(i).cross(vec3));

	MatrixN3 matN3(size, 3), mcrossN3(size, 3);
	matN3.setRandom();
	mcrossN3 = matN3.rowwise().cross(vec3);
	VERIFY_IS_APPROX(mcrossN3.row(i), matN3.row(i).cross(vec3));
}

EIGEN_DECLARE_TEST(geo_orthomethods)
{
	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_1(orthomethods_3<float>());
		CALL_SUBTEST_2(orthomethods_3<double>());
		CALL_SUBTEST_4(orthomethods_3<std::complex<double>>());
		CALL_SUBTEST_1((orthomethods<float, 2>()));
		CALL_SUBTEST_2((orthomethods<double, 2>()));
		CALL_SUBTEST_1((orthomethods<float, 3>()));
		CALL_SUBTEST_2((orthomethods<double, 3>()));
		CALL_SUBTEST_3((orthomethods<float, 7>()));
		CALL_SUBTEST_4((orthomethods<std::complex<double>, 8>()));
		CALL_SUBTEST_5((orthomethods<float, Dynamic>(36)));
		CALL_SUBTEST_6((orthomethods<double, Dynamic>(35)));
	}
}
